math (final trig problem)

posted by .

Solve for x on the interval [0,π/2):

cos^3(2x) + 3cos^2(2x) + 3cos(2x) = 4

I havent done trig for a while so what exactly does that mean in solving for x on that interval and how would i go about doing that?

Where are you getting these tough trig questions??

how about letting cos 2x = t
then your equation becomes
t^3 + 3t^2 + 3t - 4 = 0

using Newton's Method I was able to come up with ONE real root , t=.709976

so cos 2x = .709976
for 2x= .7813322 radians
and finally by dividing by 2
x = appr. .39

You can factorize the cubic equation Reiny gave above:

t^3 + 3t^2 + 3t - 4 = 0 --->

(t+1)^3 = 5 --->

t = -1 + 5^(1/3)

Count, now that was clever.
good for you to recognize the sequence
1,3,3,(1) in Pascal's triangle.

Similar Questions

1. Trig

prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= sinx^2 ^3 = (1-cosX^2)^3 = (1-2CosX^2 + cos^4) (1-cosX^2) then multiply that out 1-2CosX^2 + cos^4 - cosX^2 + 2cos^4 -cos^6 add that on the left to the cos^6, and …
2. Maths

Solve this equation fo rx in the interval 0<=x<=360 3sinxtanx=8 I would do it this way: sinxtanx = 8/3 sinx(sinx/cosx)=8/3 sin^2x/cosx = 8/3 (1-cos^2x)/cosx=8/3 cross-multiply 3 - 3cos^2x = 8cosx 3cos^2x + 8cosx - 3 = 0 (3cosx-1)(cosx+3)=0 …
3. math (trig)

i have some problems doing trig the first one is: Show that cos(x/2) sin(3x/2) = ½(sinx + sin2x) i know that you are supposed to substitute all those trig function things in it but i kind of forgot how to the only that i can see substituting …
4. Math - Trig Substitution

How can I solve the integral of x^3√(9-x^2) dx using trigonometric substitution?
5. trig

I need help with finding the amplitude, period, and the interval. y=4-3cos(x-pi)
6. Solving Trig equation

Solve the trig equation exactly in the interval 0≤x≤2π. tan x + tan π/3 ------------------ = square root 3 1 - tan x tan π/3
7. Trig

Solve the trig equation exactly over the indicated interval. tanθ = 0, all real numbers I know the answer is πn, but I don't understand how they got this. I get that tanθ = 0 on π and 2π on the unit circle, …
8. Trigonometry

Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 …
9. trig

Find all solutions in the interval [0,2π) for cos(x - π/6) = 1 + cos(x + π/6). Show work, please and state in solution set.
10. Calculus Question! ASAP!

Hello! I have this problem: x(dx)/sqrt(9-x^2) I was wondering why I can't use trig substitution and substitute sqrt(9-x^2) for sqrt(1-sec^2) and having: integral x = 3sin(theta) dx = 3cos(theta)d(theata) integral 3sin(theta)(3cos(theta))/3cos(theta) …

More Similar Questions